Question

Write your answer as a power or as a product of powers. $$ \left(5 b^{2}\right)^{3}\left(\frac{1}{2} b^{3}\right)^{2} $$

Short answer

The simplified answer in terms of powers is \(31.25*b^{12}\)

Step-by-step solution

Applying power of a power property

Start by applying the power of a power property, which gives \((5^3) * (b^{2*3}) = 125 * b^6\). Similarly, apply this rule to the next bracket yielding \((\(\frac{1}{2}\)^2 * b^{3*2}) = \(\frac{1}{4}\) * b^6\)

Applying power of a product property

Now use the power of a product property to multiply both results. This results in \(125*b^6 * \(\frac{1}{4}\)*b^6 = (125*\(\frac{1}{4}\)) * b^{6 + 6} = 31.25*b^{12}\)

Final simplification

After simplifying, the expression is reduced to \(31.25*b^{12}\)